Imprecise probabilities in engineering analyses

被引:369
作者
Beer, Michael [1 ]
Ferson, Scott [2 ]
Kreinovich, Vladik [3 ]
机构
[1] Univ Liverpool, Sch Engn, Inst Risk & Uncertainty, Liverpool L69 3GQ, Merseyside, England
[2] Appl Biomath, Setauket, NY 11733 USA
[3] Univ Texas El Paso, Dept Comp Sci, El Paso, TX 79968 USA
基金
美国国家卫生研究院; 美国国家科学基金会;
关键词
Uncertainty modeling; Imprecise probabilities; Evidence theory; Probability bounds analysis; Fuzzy probabilities; FUZZY RANDOM-VARIABLES; STRUCTURAL COLLAPSE SIMULATION; AMBIENT MODAL IDENTIFICATION; TIME-DEPENDENT RELIABILITY; EPISTEMIC UNCERTAINTY; SENSITIVITY-ANALYSIS; MODEL VALIDATION; STRONG LAW; OFFSHORE STRUCTURES; FREQUENCY-DOMAIN;
D O I
10.1016/j.ymssp.2013.01.024
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
Probabilistic uncertainty and imprecision in structural parameters and in environmental conditions and loads are challenging phenomena in engineering analyses. They require appropriate mathematical modeling and quantification to obtain realistic results when predicting the behavior and reliability of engineering structures and systems. But the modeling and quantification is complicated by the characteristics of the available information, which involves, for example, sparse data, poor measurements and subjective information. This raises the question whether the available information is sufficient for probabilistic modeling or rather suggests a set-theoretical approach. The framework of imprecise probabilities provides a mathematical basis to deal with these problems which involve both probabilistic and non-probabilistic information. A common feature of the various concepts of imprecise probabilities is the consideration of an entire set of probabilistic models in one analysis. The theoretical differences between the concepts mainly concern the mathematical description of the set of probabilistic models and the connection to the probabilistic models involved. This paper provides an overview on developments which involve imprecise probabilities for the solution of engineering problems. Evidence theory, probability bounds analysis with p-boxes, and fuzzy probabilities are discussed with emphasis on their key features and on their relationships to one another. This paper was especially prepared for this special issue and reflects, in various ways, the thinking and presentation preferences of the authors, who are also the guest editors for this special issue. (c) 2013 Elsevier Ltd. All rights reserved.
引用
收藏
页码:4 / 29
页数:26
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